Docs: normalize use of support level badges (#6159)

* Remove badges for deprecated umbrella 'google-cloud' package.

* Clarify support levels.

- Add explicit section to support linking from sub-package README badges.
- Move explanatory text for a support level above the list of packages
  at that level.

* Normalize use of support-level badges in READMEs.

- Note that 'error_reporting/README.rst' and 'monitoring/README.rst' are
  undergoing other edits;  they are left out here to avoid conflicts.

* Use 'General Avaialblity' for support level.

Fix linkx in related API READMEs.

* Fix links for alpha support in API READMEs.

* Fix links for beta support in API READMEs.

README.rst

@@ -1,7 +1,7 @@
 Python Client for Google Cloud Firestore
 ========================================
 
-|pypi| |versions|
+|beta| |pypi| |versions|
 
 The `Google Cloud Firestore`_ API is a flexible, scalable
 database for mobile, web, and server development from Firebase and Google
@@ -15,6 +15,8 @@ including Cloud Functions.
 -  `Product Documentation`_
 -  `Client Library Documentation`_
 
+.. |beta| image:: https://img.shields.io/badge/support-beta-silver.svg
+   :target: https://github.com/googleapis/google-cloud-python/blob/master/README.rst#beta-support
 .. |pypi| image:: https://img.shields.io/pypi/v/google-cloud-firestore.svg
    :target: https://pypi.org/project/google-cloud-firestore/
 .. |versions| image:: https://img.shields.io/pypi/pyversions/google-cloud-firestore.svg